2x+32=2/9*x

Solution for 2x+32=2/9*x equation:

2x+32=2/9x

We move all terms to the left:

2x+32-(2/9x)=0


Domain of the equation: 9x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x-(+2/9x)+32=0

We get rid of parentheses

2x-2/9x+32=0

We multiply all the terms by the denominator


2x*9x+32*9x-2=0

Wy multiply elements

18x^2+288x-2=0

a = 18; b = 288; c = -2;
Δ = b2-4ac
Δ = 2882-4·18·(-2)
Δ = 83088
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{83088}=\sqrt{144*577}=\sqrt{144}*\sqrt{577}=12\sqrt{577}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(288)-12\sqrt{577}}{2*18}=\frac{-288-12\sqrt{577}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(288)+12\sqrt{577}}{2*18}=\frac{-288+12\sqrt{577}}{36}
$